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3 marksVectors

CAPE Pure Mathematics Unit 1 · May/June 2000 · Paper 2 · Question 4(b)(i)

A parallelogram OABC has diagonals intersecting at D. The position vectors of A and C relative to O are -4i + 7j and 3i + 4j respectively. A diagram illustrates the parallelogram.

Determine a unit vector in the direction of OC.

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Other parts of this question

  1. 4(a)(i)Express cos 4θ in terms of cos 2θ.[2 marks]
  2. 4(a)(ii)Hence, solve the equation cos 4θ + 3 cos 2θ - 1 = 0, for 0 < θ < π.[10 marks]
  3. 4(b)(ii)Find, by calculation, the position vector of D.[5 marks]
  4. 4(b)(iii)Show that OE and OC are perpendicular.[5 marks]

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